Abstract: We present results of the Relic Axion Dark-Matter Exploratory Setup (RADES), a detector which is part of the CERN Axion Solar Telescope (CAST), searching for axion dark matter in the 34.67 μeV mass range. A radio frequency cavity consisting of 5 sub-cavities coupled by inductive irises took physics data inside the CAST dipole magnet for the first time using this filter-like haloscope geometry. An exclusion limit with a 95% credibility level on the axion-photon coupling constant of g(a gamma) greater than or similar to 4 x 10(-13) GeV-1 over a mass range of 34.6738 μeV < m(a)< 34.6771 μeV is set. This constitutes a significant improvement over the current strongest limit set by CAST at this mass and is at the same time one of the most sensitive direct searches for an axion dark matter candidate above the mass of 25 μeV. The results also demonstrate the feasibility of exploring a wider mass range around the value probed by CAST-RADES in this work using similar coherent resonant cavities.